### Sanda María López Velasco

On the one hand, the well-known logic BN4 was defined by R.T. Brady in 1982 and can be considered as the 4-valued logic of the relevant conditional. On the other hand, Routley-Meyer type ternary relational semantics is the semantics introduced by these authors in order to model the logic of relevance. Part of my current research involves applying a R-M semantics to different logics built upon some variants of MBN4 (the matrix of BN4) which verify the Routley and Meyer basic logic B.

The aim of this talk is to display these logics briefly and the reason why they could be of some interest. I will also explain how a R-M semantics can be applied to them. Considering this, I will provide a general outline of the soundness and completeness theorems, valid for all these logics, and focus on the (corresponding) postulates proofs, which on the contrary need to be specified in each of these logics.